Question

If 50 litres of milk costs Rs 1675, what is the cost of $35\dfrac{1}{2}$ litres of milk?

Answer 1

Hint: To find the cost of $35\dfrac{1}{2}$ litres of milk, we will use the unitary method. Using this method, we can find the cost of 1 litre of milk by dividing Rs 1675 by 50. Then, we can find the cost of $35\dfrac{1}{2}$ litres of milk by multiplying the cost of 1 litre of milk with $35\dfrac{1}{2}$ .

Complete step by step solution:
We have to find the cost of $35\dfrac{1}{2}$ litres of milk. Let us find the cost of 1 litres of milk using the unitary method. We are given that 50 litres of milk costs Rs 1675.
$\Rightarrow 50\text{L}=\text{Rs}.1675$
Therefore, the cost of 1 litre of milk can be found by dividing 1675 by 50.
$\Rightarrow 1\text{L}=\text{Rs}\dfrac{1675}{50}$
Now, we have to find the cost of $35\dfrac{1}{2}$ . For this, we have to multiply the cost of 1 litre of milk by $35\dfrac{1}{2}$ .
\[\Rightarrow 35\dfrac{1}{2}\text{L}=\dfrac{1675}{50}\times 35\dfrac{1}{2}\]
Let us convert the mixed fraction $35\dfrac{1}{2}$ into fractional form. We know that a mixed fraction of the form $Q\dfrac{R}{d}$ is converted into its fractional form by $\dfrac{Q\times d+R}{d}$ . Therefore, we can write $35\dfrac{1}{2}$ as
\[\begin{align}
  & \Rightarrow 35\dfrac{1}{2}\text{L}=\dfrac{1675}{50}\times \dfrac{35\times 2+1}{2} \\
 & \Rightarrow 35\dfrac{1}{2}\text{L}=\dfrac{1675}{50}\times \dfrac{70+1}{2} \\
 & \Rightarrow 35\dfrac{1}{2}\text{L}=\dfrac{1675}{50}\times \dfrac{71}{2} \\
\end{align}\]
Let us cancel the common factor 25 from the numerator and the denominator.
\[\Rightarrow 35\dfrac{1}{2}\text{L}=\dfrac{{{\require{cancel}\cancel{1675}}^{67}}}{{{\require{cancel}\cancel{50}}^{2}}}\times \dfrac{71}{2}\]
We can write the result of above simplification as
\[\begin{align}
  & \Rightarrow 35\dfrac{1}{2}\text{L}=\dfrac{67}{2}\times \dfrac{71}{2} \\
 & \Rightarrow 35\dfrac{1}{2}\text{L}=\dfrac{4757}{4} \\
\end{align}\]
Now, we have to divide 4757 by 4.
\[\Rightarrow 35\dfrac{1}{2}\text{L}=\text{Rs }1189.25\]
Hence, the cost of $35\dfrac{1}{2}$ litres of milk is Rs 1189.25.

Note: Students have a chance of making mistakes when applying unitary methods. They may find the cost of 1 litre of milk by multiplying Rs 1675 by 50 which leads to wrong result. Students must never forget to write the units at the end.